Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?potrs

Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix.

Syntax

call spotrs
(
uplo
,
n
,
nrhs
,
a
,
lda
,
b
,
ldb
,
info
)
call dpotrs
(
uplo
,
n
,
nrhs
,
a
,
lda
,
b
,
ldb
,
info
)
call cpotrs
(
uplo
,
n
,
nrhs
,
a
,
lda
,
b
,
ldb
,
info
)
call zpotrs
(
uplo
,
n
,
nrhs
,
a
,
lda
,
b
,
ldb
,
info
)
call potrs
(
a
,
b
[
,
uplo
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine solves for
X
the system of linear equations
A*X
=
B
with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix
A
, given the Cholesky factorization of
A
:
A
=
U
T
*U
for real data,
A
=
U
H
*U
for complex data
if
uplo
=
'U'
A
=
L*L
T
for real data,
A
=
L*L
H
for complex data
if
uplo
=
'L'
where
L
is a lower triangular matrix and
U
is upper triangular. The system is solved with multiple right-hand sides stored in the columns of the matrix
B
.
Before calling this routine, you must call ?potrf to compute the Cholesky factorization of
A
.
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
Indicates how the input matrix
A
has been factored:
If
uplo
=
'U'
,
U
is stored, where
A
=
U
T
*
U
for real data,
A
=
U
H
*
U
for complex data.
If
uplo
=
'L'
,
L
is stored, where
A
=
L
*
L
T
for real data,
A
=
L
*
L
H
for complex data.